(BQ) Part 2 book Intermediate microeconomics - A modern approach has contents: Auctions, technology, profit maximization, cost minimization, cost curves, firm supply, industry supply, monopoly behavior, factor markets, oligopoly, game theory,... and other contents.
CHAPTER 17 AUCTIONS Auctions are one of the oldest form of markets, dating back to at least 500 BC Today, all sorts of commodities, from used computers to fresh flowers, are sold using auctions Economists became interested in auctions in the early 1970s when the OPEC oil cartel raised the price of oil The U.S Department of the Interior decided to hold auctions to sell the right to drill in coastal areas that were expected to contain vast amounts of oil The government asked economists how to design these auctions, and private firms hired economists as consultants to help them design a bidding strategy This effort prompted considerable research in auction design and strategy More recently, the Federal Communications Commission (FCC) decided to auction off parts of the radio spectrum for use by cellular phones, personal digital assistants, and other communication devices Again, economists played a major role in the design of both the auctions and the strategies used by the bidders These auctions were hailed as very successful public policy, resulting in revenues to the U.S government of over twenty-three billion dollars to date Other countries have also used auctions for privatization projects For example, Australia sold off several government-owned electricity plants, and New Zealand auctioned off parts of its state-owned telephone system 316 AUCTIONS (Ch 17) Consumer-oriented auctions have also experienced something of a renaissance on the Internet There are hundreds of auctions on the Internet, selling collectibles, computer equipment, travel services, and other items OnSale claims to be the largest, reporting over forty-one million dollars worth of merchandise sold in 1997 17.1 Classification of Auctions The economic classification of auctions involves two considerations: first, what is the nature of the good that is being auctioned, and second, what are the rules of bidding? With respect to the nature of the good, economists distinguish between private-value auctions and common-value auctions In a private-value auction, each participant has a potentially different value for the good in question A particular piece of art may be worth $500 to one collector, $200 to another, and $50 to yet another, depending on their taste In a common-value auction, the good in question is worth essentially the same amount to every bidder, although the bidders may have different estimates of that common value The auction for off-shore drilling rights described above had this characteristic: a given tract either had a certain amount of oil or not Different oil companies may have had different estimates about how much oil was there, based on the outcomes of their geological surveys, but the oil had the same market value regardless of who won the auction We will spend most of the time in this chapter discussing private-value auctions, since they are the most familiar case At the end of the chapter, we will describe some of the features of common-value auctions Bidding Rules The most prevalent form of bidding structure for an auction is the English auction The auctioneer starts with a reserve price, which is the lowest price at which the seller of the good will part with it.1 Bidders successively offer higher prices; generally each bid must exceed the previous bid by some minimal bid increment When no participant is willing to increase the bid further, the item is awarded to the highest bidder Another form of auction is known as a Dutch auction, due to its use in the Netherlands for selling cheese and fresh flowers In this case the auctioneer starts with a high price and gradually lowers it by steps until someone is willing to buy the item In practice, the “auctioneer” is often a mechanical device like a dial with a pointer which rotates to lower and See the footnote about “reservation price” in Chapter AUCTION DESIGN 317 lower values as the auction progresses Dutch auctions can proceed very rapidly, which is one of their chief virtues Yet a third form of auctions is a sealed-bid auction In this type of auction, each bidder writes down a bid on a slip of paper and seals it in an envelope The envelopes are collected and opened, and the good is awarded to the person with the highest bid who then pays the auctioneer the amount that he or she bid If there is a reserve price, and all bids are lower than the reserve price, then no one may receive the item Sealed-bid auctions are commonly used for construction work The person who wants the construction work done requests bids from several contractors with the understanding that the job will be awarded to the contractor with the lowest bid Finally, we consider a variant on the sealed bid-auction that is known as the philatelist auction or Vickrey auction The first name is due to the fact that this auction form was originally used by stamp collectors; the second name is in honor of William Vickrey, who received the 1996 Nobel prize for his pioneering work in analyzing auctions The Vickrey auction is like the sealed-bid auction, with one critical difference: the good is awarded to the highest bidder, but at the second-highest price In other words, the person who bids the most gets the good, but he or she only has to pay the bid made by the second-highest bidder Though at first this sounds like a rather strange auction form, we will see below that it has some very nice properties 17.2 Auction Design Let us suppose that we have a single item to auction off and that there are n bidders with (private) values v1 , , For simplicity, we assume that the values are all positive and that the seller has a zero value Our goal is to choose an auction form to sell this item This is a special case of an economic mechanism design problem In the case of the auction there are two natural goals that we might have in mind: • Pareto efficiency Design an auction that results in a Pareto efficient outcome • Profit maximization Design an auction that yields the highest expected profit to the seller Profit maximization seems pretty straightforward, but what does Pareto efficiency mean in this context? It is not hard to see that Pareto efficiency requires that the good be assigned to the person with the highest value To see this, suppose that person has the highest value and person has 318 AUCTIONS (Ch 17) some lower value for the good If person receives the good, then there is an easy way to make both and better off: transfer the good from person to person and have person pay person some price p that lies between v1 and v2 This shows that assigning the good to anyone but the person who has the highest value cannot be Pareto efficient If the seller knows the values v1 , , the auction design problem is pretty trivial In the case of profit maximization, the seller should just award the item to the person with the highest value and charge him or her that value If the desired goal is Pareto efficiency, the person with the highest value should still get the good, but the price paid could be any amount between that person’s value and zero, since the distribution of the surplus does not matter for Pareto efficiency The more interesting case is when the seller does not know the buyers’ values How can one achieve efficiency or profit maximization in this case? First consider Pareto efficiency It is not hard to see that an English auction achieves the desired outcome: the person with the highest value will end up with the good It requires only a little more thought to determine the price that this person will pay: it will be the value of the second-highest bidder plus, perhaps, the minimal bid increment Think of a specific case where the highest value is, say $100, the secondhighest value is $80, and the bid increment is, say, $5 Then the person with the $100 valuation would be willing to bid $85, while the person with the $80 value would not Just as we claimed, the person with the highest valuation gets the good, at the second highest price (plus, perhaps, the bid increment) (We keep saying “perhaps” since if both players bid $80 there would be a tie and the exact outcome would depend on the rule used for tie-breaking.) What about profit maximization? This case turns out to be more difficult to analyze since it depends on the beliefs that the seller has about the buyers’ valuations To see how this works, suppose that there are just two bidders either of whom could have a value of $10 or $100 for the item in question Assume these two cases are equally likely, so that there are four equally probable arrangements for the values of bidders and 2: (10,10), (10,100), (100,10), (100,100) Finally, suppose that the minimal bid increment is $1 and that ties are resolved by flipping a coin In this example, the winning bids in the four cases described above will be (10,11,11,100) and the bidder with the highest value will always get the good The expected revenue to the seller is $33 = 14 (10 + 11 + 11 + 100) Can the seller better than this? Yes, if he sets an appropriate reservation price In this case, the profit-maximizing reservation price is $100 Three-quarters of the time, the seller will sell the item for this price, and one-quarter of the time there will be no winning bid This yields an expected revenue of $75, much higher than the expected revenue yielded by the English auction with no reservation price Note that this policy is not Pareto efficient, since one-quarter of the time AUCTION DESIGN 319 no one gets the good This is analogous to the deadweight loss of monopoly and arises for exactly the same reason The addition of the reservation price is very important if you are interested in profit maximization In 1990, the New Zealand government auctioned off some of the spectrum for use by radio, television, and cellular telephones, using a Vickrey auction In one case, the winning bid was NZ$100,000, but the second-highest bid was only NZ$6! This auction may have led to a Pareto efficient outcome, but it was certainly not revenue maximizing! We have seen that the English auction with a zero reservation price guarantees Pareto efficiency What about the Dutch auction? The answer here is not necessarily To see this, consider a case with two bidders who have values of $100 and $80 If the high-value person believes (erroneously!) that the second-highest value is $70, he or she would plan to wait until the auctioneer reached, say, $75 before bidding But, by then, it would be too late—the person with the second-highest value would have already bought the good at $80 In general, there is no guarantee that the good will be awarded to the person with the highest valuation The same holds for the case of a sealed-bid auction The optimal bid for each of the agents depends on their beliefs about the values of the other agents If those beliefs are inaccurate, the good may easily end up being awarded to someone who does not have the highest valuation.2 Finally, we consider the Vickrey auction—the variant on the sealed-bid auction where the highest bidder gets the item, but only has to pay the second-highest price First we observe that if everyone bids their true value for the good in question, the item will end up being awarded to the person with the highest value, who will pay a price equal to that of the person with the secondhighest value This is essentially the same as the outcome of the English auction (up to the bid increment, which can be arbitrarily small) But is it optimal to state your true value in a Vickrey auction? We saw that for the standard sealed-bid auction, this is not generally the case But the Vickrey auction is different: the surprising answer is that it is always in each player’s interest to write down their true value To see why, let us look at the special case of two bidders, who have values v1 and v2 and write down bids of b1 and b2 The expected payoff to bidder is: Prob(b1 ≥ b2 )[v1 − b2 ], On the other hand, if all players’ beliefs are accurate, on average, and all bidders play optimally, the various auction forms described above turn out to yield the same allocation and the same expected price in equilibrium For a detailed analysis, see P Milgrom, “Auctions and Bidding: a Primer,” Journal of Economic Perspectives, 3(3), 1989, 3–22, and P Klemperer, “Auction Theory: A Guide to the Literature,” Economic Surveys, 13(3), 1999, 227–286 320 AUCTIONS (Ch 17) where “Prob” stands for “probability.” The first term in this expression is the probability that bidder has the highest bid; the second term is the consumer surplus that bidder enjoys if he wins (If b1 < b2 , then bidder gets a surplus of 0, so there is no need to consider the term containing Prob(b1 ≤ b2 ).) Suppose that v1 > b2 Then bidder wants to make the probability of winning as large as possible, which he can by setting b1 = v1 Suppose, on the other hand, that v1 < b2 Then bidder wants to make the probability of winning as small as possible, which he can by setting b1 = v1 In either case, an optimal strategy for bidder is to set his bid equal to his true value! Honesty is the best policy at least in a Vickrey auction! The interesting feature of the Vickrey auction is that it achieves essentially the same outcome as an English auction, but without the iteration This is apparently why it was used by stamp collectors They sold stamps at their conventions using English auctions and via their newsletters using sealed-bid auctions Someone noticed that the sealed-bid auction would mimic the outcome of the English auctions if they used the second-highest bid rule But it was left to Vickrey to conduct the full-fledged analysis of the philatelist auction and show that truth-telling was the optimal strategy and that the philatelist auction was equivalent to the English auction 17.3 Other Auction Forms The Vickrey auction was thought to be only of limited interest until online auctions became popular The world’s largest online auction house, eBay, claims to have almost 30 million registered users who, in 2000, traded $5 billion worth of merchandise Auctions run by eBay last for several days, or even weeks, and it is inconvenient for users to monitor the auction process continually In order to avoid constant monitoring, eBay introduced an automated bidding agent, which they call a proxy bidder Users tell their bidding agent the most they are willing to pay for an item and an initial bid As the bidding progresses, the agent automatically increases a participant’s bid by the minimal bid increment when necessary, as long as this doesn’t raise the participant’s bid over his or her maximum Essentially this is a Vickrey auction: each user reveals to their bidding agent the maximum price he or she is willing to pay In theory, the participant who enters the highest bid will win the item but will only have to pay the second-highest bid (plus a minimal bid increment to break the tie.) According to the analysis in the text, each bidder has an incentive to reveal his or her true value for the item being sold In practice, bidder behavior is a bit different than that predicted by the Vickrey model Often bidders wait until close to the end of the auction to enter their bids This behavior appears to be for two distinct reasons: a OTHER AUCTION FORMS 321 reluctance to reveal interest too early in the game, and the hope to snatch up a bargain in an auction with few participants Nevertheless, the bidding agent model seems to serve users very well The Vickrey auction, which was once thought to be only of theoretical interest, is now the preferred method of bidding for the world’s largest online auction house! There are even more exotic auction designs in use One peculiar example is the escalation auction In this type of auction, the highest bidder wins the item, but the highest and the second-highest bidders both have to pay the amount they bid Suppose, for example, that you auction off dollar to a number of bidders under the escalation auction rules Typically a few people bid 10 or 15 cents, but eventually most of the bidders drop out When the highest bid approaches dollar, the remaining bidders begin to catch on to the problem they face If one has bid 90 cents, and the other 85 cents, the low bidder realizes that if he stays put, he will pay 85 cents and get nothing but, if he escalates to 95 cents, he will walk away with a nickel But once he has done this, the bidder who was at 90 cents can reason the same way In fact, it is in her interest to bid over a dollar If, for example, she bids $1.05 (and wins), she will lose only cents rather than 90 cents! It’s not uncommon to see the winning bid end up at $5 or $6 A somewhat related auction is the everyone pays auction Think of a crooked politician who announces that he will sell his vote under the following conditions: all the lobbyists contribute to his campaign, but he will vote for the appropriations favored by the highest contributor This is essentially an auction where everyone pays but only the high bidder gets what she wants! EXAMPLE: Late Bidding on eBay According to standard auction theory eBay’s proxy bidder should induce people to bid their true value for an item The highest bidder wins at (essentially) the second highest bid, just as in a Vickrey auction But it doesn’t work quite like that in practice In many auctions, participants wait until virtually the last minute to place their bids In one study, 37 percent of the auctions had bids in the last minute and 12 percent had bids in the last 10 seconds Why we see so many “late bids”? There are at least two theories to explain this phenomenon Patrick Bajari and Ali Horta¸csu, two auction experts, argue that for certain sorts of auctions, people don’t want to bid early to avoid driving up the selling price EBay typically displays the bidder identification and actual bids (not the maximum bids) for items being sold If you are an expert on rare stamps, with a well-known eBay member name, you may want to hold back placing your bid so as not to reveal that you are interested in a particular stamp 322 AUCTIONS (Ch 17) This explanation makes a lot of sense for collectibles such as stamps and coins, but late bidding also occurs in auctions for generic items, such as computer parts Al Roth and Axel Ockenfels suggest that late bidding is a way to avoiding bidding wars Suppose that you and someone else are bidding for a Pez dispenser with a seller’s reserve price of $2 It happens that you each value the dispenser at $10 If you both bid early, stating your true maximum value of $10, then even if the tie is resolved in your favor you end up paying $10—since that is also the other bidder’s maximum value You may “win” but you don’t get any consumer surplus! Alternatively, suppose that each of you waits until the auction is almost over and then bids $10 in the last possible seconds of the auction (At eBay, this is called “sniping.”) In this case, there’s a good chance that one of the bids won’t get through, so the winner ends up paying only the seller’s reserve price of $2 Bidding high at the last minute introduces some randomness into the outcome One of the players gets a great deal and the other gets nothing But that’s not necessarily so bad: if they both bid early, one of the players ends up paying his full value and the other gets nothing In this analysis, the late bidding is a form of “implicit collusion.” By waiting to bid, and allowing chance to play a role, bidders can end up doing substantially better on average than they by bidding early 17.4 Position Auctions A position auction is a way to auction off positions, such as a position in a line or a position on a web page The defining characteristic is that all players rank the positions in the same way, but they may value the positions differently Everybody would agree that it is better to be in the front of the line than further back, but they could be willing to pay different amounts to be first in line One prominent example of a position auction is the auction used by search engine providers such as Google, Microsoft, and Yahoo to sell ads In this case all advertisers agree that being in the top position is best, the second from the top position is second best, and so on However, the advertisers are often selling different things, so the expected profit that they will get from a visitor to their web page will differ Here we describe a simplified version of these online ad auctions Details differ across search engines, but the model below captures the general behavior We suppose that there are s = 1, , S slots where ads can be displayed Let xs denote the number of clicks that an ad can expect to receive in slot s We assume that slots are ordered with respect to the number of clicks they are likely to receive, so x1 > x2 > · · · > xS POSITION AUCTIONS 323 Each of the advertisers has a value per click, which is related to the expected profit it can get from a visitor to its web site Let vs be the value per click of the advertiser whose ad is shown in slot s Each advertiser states a bid, bs , which is interpreted as the amount it is willing to pay for slot s The best slot (slot 1) is awarded to the advertiser with the highest bid, the second-best slot (slot 2) is awarded to the advertiser with the second highest bid, and so on The price that an advertiser pays for a bid is determined by the bid of the advertiser below him This is a variation on the Vickrey auction model described earlier and is sometimes known as a generalized second price auction or GSP In the GSP, advertiser pays b2 per click, advertiser pays b3 per click, and so on The rationale for this arrangement is that if an advertiser paid the price it bid, it would have an incentive to cut its bid until it just beat the advertiser below it By setting the payment of the advertiser in slot s to be the bid of the advertiser in slot s + 1, each advertiser ends up paying the minimum bid necessary to retain its position Putting these pieces together, we see that the profit of the advertiser in slot s is (vs − bs+1 )xs This is just the value of the clicks minus the cost of the clicks that an advertiser receives What is the equilibrium of this auction? Extrapolating from the Vickrey auction, one might speculate that each advertiser should bid its true value This is true if there is only one slot being auctioned, but is false in general Two Bidders Let us look at the case of slots and bidders We assume that the high bidder gets x1 clicks and pays the bid of the second highest bidder b2 The second highest bidder gets slot and pays a reserve price r Suppose your value is v and you bid b If b > b2 you get a payoff of (v − b2 )x1 and if b ≤ b2 you get a payoff of (v − r)x2 Your expected payoff is then Prob(b > b2 )(v − b2 )x1 + [1 − Prob(b > b2)](v − r)x2 We can rearrange your expected payoff to be (v − r)x2 + Prob(b > b2 )[v(x1 − x2 ) + rx2 − b2 x1 ] (17.1) Note that when the term in the brackets is positive (i.e., you make a profit), you want the probability that b > b2 to be as large as possible, and when the term is negative (you make a loss) you want the probability that b > b2 to be as small as possible 324 AUCTIONS (Ch 17) However, this can easily be arranged Simply choose a bid according to this formula: bx1 = v(x1 − x2 ) + rx2 Now it is easy to check that when b > b2 , the bracketed term in expression (17.1) is positive and when b ≤ b2 the bracketed term in (17.1) is negative or zero Hence this bid will win the auction exactly when you want to win and lose it exactly when you want to lose Note that this bidding rule is a dominant strategy: each bidder wants to bid according to this formula, regardless of what the other player bids This means, of course, that the auction ends up putting the bidder with the highest value in first place It is also easy to interpret the bid If there are two bidders and two slots, the second highest bidder will always get the second slot and end up paying rx2 The contest is about the extra clicks that the highest bidder gets The bidder who has the highest value will win those clicks, but that bidder only has to pay the minimum amount necessary to beat the second highest bidder We see that in this auction, you don’t want to bid your true value per click, but you want to bid an amount that reflects your true value of the incremental clicks you are getting More Than Two Bidders What happens if there are more than two bidders? In this case, there will typically not be a dominant strategy equilibrium, but there will be a equilibrium in prices Let us look at a situation with slots and bidders The bidder in slot pays a reservation price r In equilibrium, the bidder won’t want to move up to slot 2, so (v3 − r)x3 ≥ (v3 − p2 )x2 or v3 (x2 − x3 ) ≤ p2 x2 − rx3 This inequality says that if the bidder prefers position to position 2, the value of the extra clicks it gets in position must be less than the cost of those extra clicks This inequality gives us a bound on the cost of clicks in position 2: p2 x2 ≤ rx3 + v3 (x2 − x3 ) (17.2) Applying the same argument to the bidder in position 2, we have p1 x1 ≤ p2 x2 + v2 (x1 − x2 ) (17.3) A26 ANSWERS much smaller time periods seems to indicate that players rarely use this strategy 28.6 The equilibrium has player B choosing left and player A choosing top Player B prefers to move first since that results in a payoff of versus a payoff of (Note, however, that moving first is not always advantageous in a sequential game Can you think of an example?) 29 Game Applications 29.1 In a Nash equilibrium, each player is making a best response to the other player’s best response In a dominant strategy equilibrium, each player’s choice is a best response to any choice the other player makes 29.2 No, because when r = 1/3 there is an infinity of best responses, not a single one, as is required for the mathematical definition of a function 29.3 Not necessarily; it depends on the payoffs of the game In chicken if both choose to drive straight they receive the worst payoff 29.4 It is row’s expected payoff in the equilibrium strategy of kicking to the left with probability 7, while column jumps to the left with probability We have to sum the payoffs to row over four events: the probability row kicks left and column defends left × row’s payoff in this case + probability row kicks right and column defends left × row’s payoff in this case, and so on The numbers are (.7)(.6)50 + (.7)(.4)80 + (.3)(.6)90 + (.3)(.4)20 = 62 29.5 He means that he will bid low in order to get the contract, but then charge high prices subsequently for any changes The client has to go along, since it is costly for him to switch in the middle of a job 30 Behavioral Economics 30.1 The first group is more likely to buy, due to the “framing effect.” 30.2 The “bracketing effect” makes it likely that the meals chosen by Mary will have more variety 30.3 From the viewpoint of classical consumer theory, more choice is better But it is certainly possible that too much choice could confuse the employees, so 10 might be a safer choice If you did decide to offer 50 mutual funds, it would be a good idea to group them into a relatively small number of categories ANSWERS A27 30.4 The probability of heads coming up times in a row is 12 × 12 × 12 = = 125 The probability of tails coming up in a row is also 125, so the probability of a run of heads or tails is 25 30.5 It is called “time inconsistency.” 31 Exchange 31.1 Yes For example, consider the allocation where one person has everything Then the other person is worse off at this allocation than he would be at an allocation where he had something 31.2 No For this would mean that at the allegedly Pareto efficient allocation there is some way to make everyone better off, contradicting the assumption of Pareto efficiency 31.3 If we know the contract curve, then any trading should end up somewhere on the curve; however, we don’t know where 31.4 Yes, but not without making someone else worse off 31.5 The value of excess demand in the remaining two markets must sum to zero 32 Production 32.1 Giving up coconut frees up $6 worth of resources that could be used to produce pounds (equals $6 worth) of fish 32.2 A higher wage would produce a steeper isoprofit line, implying that the profit maximizing level for the firm would occur at a point to the left of the current equilibrium, entailing a lower level of labor demand However, under this new budget constraint Robinson will want to supply more than the required level of labor (why?) and therefore the labor market will not be in equilibrium 32.3 Given a few assumptions, an economy that is in competitive equilibrium is Pareto efficient It is generally recognized that this is a good thing for a society since it implies that there are no opportunities to make any individual in the economy better off without hurting someone else However, it may be that the society would prefer a different distribution of welfare; that is, it may be that society prefers making one group better off at the expense of another group 32.4 He should produce more fish His marginal rate of substitution indicates that he is willing to give up two coconuts for an additional fish The A28 ANSWERS marginal rate of transformation implies that he only has to give up one coconut to get an additional fish Therefore, by giving up a single coconut (even though he would have been willing to give up two) he can have an additional fish 32.5 Both would have to work hours per day If they both work for hours per day (Robinson producing coconuts, and Friday catching fish) and give half of their total production to the other, they can produce the same output The reduction in the hours of work from to hours per day is due to rearranging production based on each individual’s comparative advantage 33 Welfare 33.1 The major shortcoming is that there are many allocations that cannot be compared—there is no way to decide between any two Pareto efficient allocations 33.2 It would have the form: W (u1 , , un ) = max{u1 , , un } 33.3 Since the Nietzschean welfare function cares only about the best off individual, welfare maxima for this allocation would typically involve one person getting everything 33.4 Suppose that this is not the case Then each individual envies someone else Let’s construct a list of who envies whom Person A envies someone— call him person B Person B in turn envies someone—say person C And so on But eventually we will find someone who envies someone who came earlier in the list Suppose the cycle is “C envies D envies E envies C.” Then consider the following swap: C gets what D has, D gets what E has, and E gets what C has Each person in the cycle gets a bundle that he prefers, and thus each person is made better off But then the original allocation couldn’t have been Pareto efficient! 33.5 First vote between x and z, and then vote between the winner (z) and y First pair x and y, and then vote between the winner (x) and z The fact that the social preferences are intransitive is responsible for this agenda-setting power 34 Externalities 34.1 True Usually, efficiency problems can be eliminated by the delineation of property rights However, when we impose property rights we are also imposing an endowment, which may have important distributional consequences ANSWERS A29 34.2 False 34.3 Come on, your roommates aren’t all bad 34.4 The government could just give away the optimal number of grazing rights Another alternative would be to sell the grazing rights (Question: how much would these rights sell for? Hint: think about rents.) The government could also impose a tax, t per cow, such that f (c∗ )/c∗ + t = a 35 Information Technology 35.1 They should be willing to pay up to $50, since this is the present value of the profit they can hope to get from that customer in the long run 35.2 Users would gravitate toward packages with the most users, since that would make it more convenient for them to exchange files and information about how to use the program 35.3 In this case the profit maximization conditions are identical If two people share a video, the producer would just double the price and make exactly the same profits 36 Public Goods 36.1 We want the sum of the marginal rates of substitution to equal the marginal cost of providing the public good The sum of the MRSs is 20 (= 10×2), and the marginal cost is 2x Thus we have the equation 2x = 20, which implies that x = 10 So the Pareto efficient number of streetlights is 10 37 Asymmetric Information 37.1 Since only the low-quality cars get exchanged in equilibrium and there is a surplus of $200 per transaction, the total surplus created is 50 × 200 = $10, 000 37.2 If the cars were assigned randomly, the average surplus per transaction would be the average willingness to pay, $1800, minus the average willingness to sell, $1500 This gives an average surplus of $300 per transaction and there are 100 transactions, so we get a total surplus of $30,000, which is much better than the market solution A30 ANSWERS 37.3 We know from the text that the optimal incentive plan takes the form s(x) = wx + K The wage w must equal the marginal product of the worker, which in this case is The constant K is chosen so that the worker’s utility at the optimal choice is u = The optimal choice of x occurs where price, 1, equals marginal cost, x, so x∗ = At this point the worker gets a utility of x∗ + K − c(x∗ ) = + K − 1/2 = 1/2 + K Since the worker’s utility must equal 0, it follows that K = −1/2 37.4 We saw in the last answer that the profits at the optimal level of production are 1/2 Since u = 0, the worker would be willing to pay 1/2 to rent the technology 37.5 If the worker is to achieve a utility level of 1, the firm would have to give the worker a lump-sum payment of 1/2 INDEX absolute value, A6 active decision, 569 ad valorem subsidy, 27, 29 ad valorem tax, 27, 298 Adobe, 686 Adobe Systems, 683 AdSense, 674 adverse selection, 722 AdWords, 674 affine function, A4 after-tax interest rate, 200, 307 aggregate demand, 270–272 aggregate excess demand, 592 aggregate excess demand function, 591 airline industry, 467 all other goods, 34 allocation, 583, 636 fair, 639–642 feasible, 583 final, 583 initial endowment, 583 allocation of resources, 12, 14 anchoring effect., 568 Apple, 673 appreciation, 206 arbitrage, 205, 214 rule, 208 Arrow’s Impossibility Theorem, 634, 642 Arrow, Kenneth, 222 asset bubble, 209 asset integration hypothesis, 573 assets, 203 assurance games, 544 asymmetric information, 719, 736 auction, 329 auctions, 315–331, 456 average cost, 378–380, 410 curve, 381 fixed, 379 long-run, 388 pricing, 453 short-run, 388 variable, 379, 381, 410 average cost function, 370 axioms, 35 backward-bending labor supply curve, 176 bad, 41, 81 Bangladesh, 737 barriers to entry, 416 battle of the sexes, 542 behavioral economics, 566 behavioral game theory, 577 Benthamite welfare function, 635 Bergson-Samuelson welfare function, 639 Bertrand competition, 512 Bertrand equilibrium, 530 best response, 538 best response curves, 538 beta, 242, 249 bid, 330 bid increment, 316 bidding agent, 320 bidding pools, 456 bliss, 43 bond, 198 borrower, 186 boundary optimum, 76 bracketing, 570 budget constraint, 20, 21, 161, 179, 183, 184, 202 line, 22, 31 set, 21, 31 bulk discounts, 465 bundles, 474 cap and trade, 433 capital, 333 financial, 333 A32 INDEX physical, 333 Capital Asset Pricing Model (CAPM), 245 capital gains, 207 capital goods, 333 carbon taxes, 433 cardinal utility, 57 cartel, 455, 513, 520, 528, 531 catastrophe bonds, 221 cell phone industry, 677 chain rule, A8 chicken, 545 Chinese economic reforms, 734 choice behavior, 567 choice under uncertainty, 232, 571 classical utilitarian, 635 Coase Theorem, 648, 649 Cobb-Douglas, 63, 82 demand, 113 preferences, 64, 72, 100 production function, 335 technology, 368 utility, 64, 93, 594 collusion, 498, 513 command mechanism, 708 commitment, 553 commitment devices, 576 common-value auctions, 316, 327 commons tragedy of, 659 commuting behavior, 68 comparative advantage, 621 comparative statics, 9, 11, 18, 95, 186, 297, 313, 352 compensated demand, 140 compensated demand curve., 156 compensating variation, 258–262, 266, 269 competitive, 588 behavior, 603 equilibrium, 590, 628 market, 5, 12, 14, 293, 345 market and Pareto efficiency, 310 complement, 111, 112, 115 gross, 112 complementarity, 674 complementary goods, 475, 678 complements, 668 complete preferences, 35, 634 composite function, A8 composite good, 21, 182 computer chips, 343 concave preferences, 82 utility function, 227 conditional factor demand, 367, 374 condominiums, 10 Congress, 197 consols, 198 constant average cost, 409 constant returns to scale, 341, 344, 355, 361, 420 constant-elasticity demand curve, 280, 443 constrained maximization, 91 constraint, A10 economic, 396 market, 396 consumer behavior, 566 consumer choice, 566 consumer preferences, 54 consumer’s surplus, 253, 313, 463 change in, 257 gross, 253 consumers’ surplus, 255, 458 consumption bundle, 21, 33 contingent, 219 externality, 603, 618 returns, 206 contextually targeted ads, 674 continuous function, 596, A2 contract curve, 586, 587 convex, 52, 227 indifference curves, 52 isoquant, 343 preferences, 77, 596, 602 set, 47 technology, 336–337 cooperative game, 498 cooperative insurance, 231 coordination games, 542 copyright, 197 corporation, 347, 734 cost, 365, 374, 378 average, 378–381, 410 average, fixed, 379 average, long-run, 388 average, variable, 379, 381, 410 fixed, 373 long run, 371 long run, average, 391 long run, marginal, 390 marginal, 380–382, 410, 440 private, 653 short run, average, 391 variable, 379, 382 costly information, 718 counterparty risk, 243 coupon, 198 Cournot equilibrium, 508, 525 model, 507–512 INDEX datacenter, 343 deadweight loss, 312, 428, 458 due to monopoly, 447, 449 due to tax, 304–306, 313 decentralized resource allocation, 624 decreasing returns to scale, 342 deferred acceptance algorithm, 328 demand curve, 3, 4, 10, 18, 107, 112, 167 curve facing the firm, 396, 397, 410 elastic, 276, 286 function, 13, 78, 95, 114 inelastic, 276 unit elastic, 276 demand curve facing the firm, 396 demanded bundle, 78 dependent variable, A1 depletable resources, 210 derivative, A6 derived factor demands, 367 diminishing marginal rate of substitution, 52 diminishing technical rate of substitution, 339 Ding, 464 direct revelation mechanism, 330 directly revealed preferred, 120 discrete good, 44, 109, 252 discriminating monopolist, 12, 14, 455– 473, 599 disequilibrium, 590 Disney, 197 Disneyland Dilemma, 476 distortionary tax, 605 distributional consequences, 647 diversification, 230 dividend, 207 dominant strategy, 324, 523, 700, 712 equilibrium, 536 dominates, 192 double markup, 494 downstream monopolist, 492 duopoly, 498, 532 game, 530 Dupuit, Emile, 468 Dutch auction, 316 eBay, 320, 326, 692 economic mechanism, 711 economic mechanism design, 317 economic mechanisms, 329 economic rent, 422–426, 437 Edgeworth box, 583, 606, 645 effective price, 264 efficiency, 15, 647 efficiency prices, 608 A33 effluent fees, 664 elasticity, 274–276, 441 and revenue, 277 demand, 286 electricity, 152 emission standards, 663 emissions licenses, 436 endogenous variable, endowment, 160, 163–164, 178, 605, 647 of consumption, 173 of time, 174 endowment income effect, 169, 171, 172, 176 Engel curve, 97, 99, 102 English auction, 316 entitlement program, 432 entry, 415–417, 437, 534 deterrence, 534 envy, 640 equation, A3 equilibrium, 3, 7, 294, 590 analysis, 292, 295 in loan market, 307 price, 6–8, 10, 18, 293–294, 313 principle, 3, 18 with taxes, 300–309 equilibrium principle, 292 equilibrium strategy, 527 equitable, 640 equivalent variation, 258–262, 266, 269 escalation auction, 321 ESS, 552 estimation of preferences, 135 everyone pays auction, 321 evolutionarily stable strategy, 552 excess burden, 306 excess demand, 14, 589, 591 excess risk aversion, 573 excessive choice, 570 existence of a competitive equilibrium, 595 exit, 415, 416, 437 exogenous variable, expected return, 234, 238, 239 expected utility, 225, 226, 573 expected utility function, 224, 232 expected value, 223, 226 expenditure share, 285 exponential discounting, 574 extensive form, 532 extensive margin, 273 external monopolist, 349 externalities, 645, 648, 665, 678, 694, 705 consumption, 644 production, 618, 644 externality, 329 A34 INDEX fab plants, 343 face value, 198 Facebook, 692 factor demand, 354, 361 inverse function, 354 factors of production, 332 fair, 640 fair allocations, 639 fairness norms, 578 FCC, 315 feasible allocation, 583 Federal Communications Commission (FCC), 315 final allocation, 583 financial assets, 203 financial capital, 333 financial contagion, 243 financial institutions, 213 financial instruments, 198 financial markets, 198, 348 First Theorem of Welfare Economics, 597, 603, 606, 617, 618, 665 first-degree price discrimination, 462, 464 first-order condition, A9 fixed cost, 373 fixed factor, 350, 360, 387, 423 fixed proportions, 40 fixed supply, 294 focal point, 543 food stamps, 29 food subsidy, 309 forest, 211 framed, 567 framing negative, 568 positive, 568 framing effects, 567 free disposal, 336 free entry, 416, 419 free rider, 699, 706, 716 full income, 174 function, A1 continuous, 596 future value, 184, 192, 202 game theory, 329, 522, 572 gasoline tax, 148 general equilibrium, 582, 606, 628 generalized second price auction, 323 Georgia Power Company, 152 Giffen good, 103–105, 114, 136, 144 Google, 322, 674 government-run monopolies, 453 Grameen Bank, 737 graph, A2 gross benefit, 253 gross complements, 112 gross consumer’s surplus, 253 gross demand, 167, 178, 589 gross demands, 161 gross substitutes, 112 Groves mechanism, 711 hawk-dove game, 551 Hicks substitution effect, 153–155, 158 hidden action, 725 hidden information, 725 homothetic preferences, 101 horizontal intercept, A5 horizontal supply curve, 294 housing rate of return on, 206 rental rate on, 206 tax treatment of, 267 hyperbolic discounting, 575 identity, A3 implicit functions, 71 implicit income, 174 implicit rental rate, 206 incentive compatibility constraint, 330, 732 incentive systems, 730 income distribution, 271 effect, 102, 137, 141–142, 156, 179, 256 expansion paths, 97–103 offer curves, 97–103 tax, 87 income elasticity of demand, 285 increasing returns to scale, 341 independence assumption, 225 independent variable, A1 index fund, 248 index numbers, 131 indexing, 133 indifference, 34 indifference curve, 36–44, 52, 585 construction of, 585 indirect revealed preference, 121, 128, 130 individualistic welfare function, 639, 643 industry equilibrium long run, 415 short run, 414 industry supply curve, 413 inelastic, 286 inferior good, 96, 106, 114, 144, 156, 163, 285 inflation expected rate of, 191 inflation rate, 190–191 INDEX information economy, 667 inframarginal, 447 initial endowment, 583, 647 installment loans, 199 insurance, 227, 723, 725 Intel, 343 intellectual property, 690 intensive margin, 273 interest rate, 183–185, 200, 207 nominal, 190, 201 real, 190, 201 interior optimum, 76 internal monopolist, 349 internalization of production externalities, 658 internalized, 651 intertemporal budget constraint, 185 choice, 182 intertemporal choices, 182 InterTrust Technology, 450 intransitive preferences, 58 intransitivity, 710 inverse demand function, 112, 113, 115, 272, 295 inverse function, A3 inverse supply function, 295, 296, 403 iPod, 672, 686 iPods, 673 Iraq, 310 isocost lines, 365 isoprofit curves, 503, 515 isoprofit lines, 351, 501, 612, 625 isoquant, 334, 343, 365 isowelfare curves, 637 iTunes, 673, 686 jewelry, 326 joint production possibilities set, 621 kinky tastes, 76 Kodak, 451 labor market, 288 supply, 172–179 supply curve, backward bending, 177 Laffer curve, 288 effect, 288, 289 Lagrange multiplier, 92 Lagrangian, 607, 630, 643, 716 Laspeyres price index, 132 quantity index, 131 Law of Demand, 147, 156 A35 law of diminishing marginal product, 339 Law of Large Numbers, 571 leisure, 175 lender, 186 level set, 59 linear demand, 443 linear function, A4 LinkedIn, 692 liquidity, 202, 205, 208 liquor licenses, 427 loans, 306 lock-in, 674 logarithm, A6 long run, 17, 340, 344, 350, 361 average cost, 388, 391 marginal costs, 390 long-run cost function, 371 equilibrium, 418 supply curve, 409, 417, 437 supply function, 407 loss averse, 573 lower envelope, 389 lump sum subsidy, 27, 31 tax, 27 luxury good, 101 luxury goods, 285 maintained hypothesis, 175 majority voting, 632 marginal change, A4 marginal cost, 380–382, 391, 410, 440 marginal product, 338, 343, 361, 486 marginal rate of substitution, 48–52, 66, 70–72, 89, 590, 622, 628 marginal rate of transformation, 620, 628 marginal revenue, 281–286, 440–441, 486 marginal revenue product, 486 marginal utility, 65–67, 70 marginal willingness to pay, 51, 114 market constraint, 396 demand, 270–272, 285, 293, 397 environment, 396 equilibrium, 590 line, 245 portfolio, 244 supply, 293 system, 14 market supply curve, 413 markup pricing, 443, 458 maturity date, 198 maximum, A9 mean, 237 A36 INDEX mean-variance model, 236 measured income, 174 median expenditure, 710 Mickey Mouse, 197 Microsoft, 322, 450 Microsoft Corporation, 402 minimax social welfare function, 636 minimum, A9 minimum efficient scale, 454, 458 minimum wage, 491 mixed strategies, 542 mixed strategy, 526, 547 model, 2, 8, 11 monitoring costs, 737 monopolist, 12, 14, 598 discriminating, 12, 14, 455–473, 599 monopolistic competition, 473–480, 484, 497 monopoly, 12, 439, 458, 485 deadweight loss, 449 government-run, 453 ineffiency, 446 natural, 453, 458 Pareto efficiency, 17 monopsony, 488–490, 495 monotonic, 52, 336, 343, A3 transformation, 55, 67, 69, 223 monotonicity, 45 moral hazard, 724 MS-DOS, 402 municipal bonds, 208 mutual fund, 247–249 mutually assured destruction, 450 MySpace, 692 Nash bargaining model, 561 Nash equilibria, 544 Nash equilibrium, 524, 532, 536, 539, 670 natural monopoly, 453, 458 necessary condition, 77 necessary good, 101 negative correlation, 242 negative framing, 568 negative monotonic function, A3 net buyer, 161 net consumer’s surplus, 253 net demand, 161, 167, 178, 589, 591 net present value, 195 net producer’s surplus, 264 net seller, 161 net supplier, 161 Netscape Communications Corporation, 684 network effect, 692 network externalities, 475, 678, 683 neutral good, 41, 81 no arbitrage condition, 205 nominal rate of interest, 190 nonconvex preferences, 82 nonconvexity, 616 nonlabor income, 173 nonlinear pricing, 465 normal good, 96, 114, 156, 163, 285 number portability, 677 numeraire, 26, 594, 611 objective function, A10 offer curves, 97–103 oil, 210 oligopoly, 497, 519, 534 online bill payment services, 677 OPEC, 148, 315, 429 opportunity cost, 23, 174, 202, 346, 416, 423 optimal choice, 73–78, 89 optimality condition, 162 optimization principle, 3, 18, 292 ordinal utility, 55 ordinary good, 103–105, 114 ordinary income effect, 169 Organization of Petroleum Exporting Countries (OPEC), 451 overconfidence., 576 overtime wage, 177 Paasche price index, 132 quantity index, 131 paradox of voting, 709 Pareto efficiency, competitive market, 310 Pareto efficient, 15–16, 18, 310–313, 317, 446, 463, 527, 536, 596–602, 607, 622, 628, 645, 665, 696 allocation, 16, 586, 601, 606, 607 competitive market, 16 discriminating monopolist, 16 monopoly, 17 rent control, 17 Pareto improvement, 15, 17, 696, 697 Pareto inefficient, 15, 697 Pareto set, 587 partial derivative, A8 partial equilibrium, 582 participation constraint, 731 partnership, 347 passing along a tax, 302 patent, 197, 449 patent portfolios, 450 patent thicket, 450 patents, 450 INDEX payoff matrix, 522 perfect complements, 40, 62, 79, 99, 107, 147, 335 perfect price discrimination, 462, 599 perfect substitutes, 38, 39, 61, 78, 99, 107, 147, 335 perfectly elastic, 302 perfectly inelastic, 302 perpetuities, 198 philatelist auction, 317 physical capital, 333 Pigouvian tax, 656, 665 pivotal, 714 pivoted and shifted budget lines, 138 pollution, 663, 704 Polonius point, 184 pooling equilibrium, 728 portfolio, 238 position auction, 322 positive affine transformation, 224 positive framing, 568 positive monotonic function, A3 preference ordering, 58, 69 strict, 34 preference(s), 34, 35, 632 axioms, 35 complete, 35 concave, 82 convex, 47 estimation, 135 maximization, 90 nonconvex, 82 over probability distributions, 219 reflexive, 35 single peaked, 709 strict, 34 transitive, 35 weak, 34 preferences recovering, 122 preliminary injunction, 451 present value, 184, 192–194, 197, 202, 215 of consumption, 192 of income, 192 of profits, 347 of the firm, 348 price allocative role of, 604 controls, 431 discrimination, 462, 467, 484 distributive role, 604 elasticity of demand, 274, 284 follower, 498 leader, 498, 504, 507 maker, 489 A37 of risk, 240, 244 offer curve, 106, 167, 598 supports, 360 taker, 397, 489 price discrimination, 469 Principle of Revealed Preference, 121 prisoner’s dilemma, 527, 530, 536, 544, 699 private costs, 652 private-value auctions, 316 probability distribution, 217 producer’s surplus, 263–264, 403, 410, 425, 458, 463 producers’ surplus, 313 product differentiation, 478 production externalities, 618, 644 function, 333, 343, 610 possibilities frontier, 619 possibilities set, 619, 621 set, 333, 343 techniques, 337 profit, 345–346, 360, 403 economic, 346 long run, 353–354 maximization, long run, 353 short run, 351–352 property rights, 647, 648, 665 proprietorship, 347 proxy bidder, 320 public good, 695, 716 public goods, 329 punishment games, 578 punishment strategy, 516 purchasing power, 137, 141, 156 pure competition, 396 pure exchange, 583 pure strategy, 525 purely competitive, 396 quality, 719 quality choice, 720 quality score, 325 quantity follower, 498 leader, 498, 507 subsidy, 27 tax, 27, 87, 298 quasi-fixed cost, 373 quasi-fixed factors, 350 quasilinear preferences, 63, 102, 115, 148, 649, 665, 698, 703 utility, 63, 256, 262 randomize, 526 A38 INDEX randomizing, 572 rank-order voting, 633 rate of change, A4 rate of exchange, 67, 77 rate of return, 215 rationing, 28, 32 Rawlsian social welfare function, 636 reaction function, 500, 502 real interest rate, 190, 202 Real Time Pricing (RTP), 152 real wage, 174 recovering preferences, 122 reflexive, 35 reflexive preferences, 634 regulatory boards, 453 reinsurance market., 221 relative prices, 593–594, 606 rent, 732, 735 control, 14 control and Pareto efficiency, 17 economic, 422–426, 437 seeking, 428 rent seeking, 437 rental rate, 346 repeated games, 536 representative consumer, 271 reservation price, 4, 16, 109, 253, 273, 286, 678, 686, 696 reserve price, 316 residual claimant, 733 residual demand curve, 506 resource allocation, 18 decentralized, 624, 627 returns to scale, 341, 374 and the cost function, 369 constant, 341, 355, 361, 420 decreasing, 342 increasing, 341 revealed preference, 120–122, 135, 154, 165, 187 revealed profitability, 356 revenue, 277 rights management, 687 risk, 241 adjusted return, 246 adjustment, 244 averse, 227 averter, 232 lover, 227, 232 neutral, 227 premium, 245 spreading, 231 risk averse, 573 risk-free asset, 238, 241 riskless arbitrage, 205 risky asset, 233–234, 238 taxation, 235 Robinson Crusoe economy, 609 rock paper scissors, 526 Rubinstein bargaining model, 561 sales tax, 27, 299 satiation, 43 sealed-bid auction, 317 search targeted ads, 674 second derivative, A7 Second Theorem of Welfare Economics, 602, 604–606, 618 second-degree price discrimination, 462, 465 second-order condition, A9 security, 198 self select, 465 self-control, 575 self-serving attribution bias, 576 separating equilibrium, 728 sequential game, 498, 532, 534, 536 sequential moves, 553 shadow prices, 608 sharecropping, 736 shareholder voting rights, 734 sheepskin effect, 730 short run, 17, 340, 344, 350, 361 average cost, 391 cost function, 371 supply curve, 437 shutdown condition, 401 signaling, 726 simultaneous game, 498 simultaneous moves, 553 single peaked preferences, 709 slope, A5 Slutsky demand function, 157 equation, 156–158, 169, 170, 179, 180, 187, 188 equation, with endowment, 171 identity, 143–145 identity, rates of change, 145 income effect, 141–142 substitution effect, 152, 153 Smith, Adam, 456 smooth function, A3 social cost, 304, 651, 653, 661, 665 social norms, 564 social preference, 632, 708 Social Security, 133 social welfare function, 635 software suite, 474, 475 solution, A3 Southwest Airlines, 464 stable equilibrium, 511 INDEX Stackelberg follower, 500 leader, 502 model, 499–504, 532 standard deviation, 237 state contingent security, 222 states of nature, 219, 220, 232 stock market, 214, 231, 348 value, 348 strategic choices, 536 strategic interaction, 497, 522, 576 strategy method, 578 strict convexity, 48, 120 strict preference, 34 Strong Axiom of Revealed Preference (SARP), 128 subsidies, 310 subsidy, 27, 32, 360 ad valorem, 27, 29 food, 309 lump sum, 27, 31 quantity, 27 substitute, 111, 115 gross, 112 substitution effect, 137, 139, 142, 153, 156 sufficient condition, 77 Sun Microsystems, 450 sunk cost, 373 sunk cost fallacy, 574 supply curve, 5–6, 10, 17, 18, 161, 168, 262, 293, 313, 410 competitive firm, 399 horizontal, 294 industry, 413 inverse, 403 long run, 407, 409, 417, 418, 437 market, 293, 413 vertical, 294 supply function, 361 inverse, 295, 296 switching costs, 674, 678 symmetric treatment, 642 systemic risk, 243 take-it-or-leave-it, 733, 736 taking bids off the wall, 326 tangent, A6 tax, 11, 32, 87, 200, 298, 313, 420 ad valorem, 27, 298 capital gains, 207 deadweight loss, 304–306, 313 gasoline, 148 lump sum, 27 on asset returns, 207 policy, 288 A39 quantity, 27, 298 reforms, 267 sales, 27, 299 value, 298 welfare implications, 604 taxi licenses, 424 technical rate of substitution, 344, 365 technical rate of substitution (TRS), 338 technological constraints, 332, 333, 343, 395 technology convex, 336–337 perfect complements, 368 perfect substitutes, 368 third-degree price discrimination, 462, 469 time behavior over, 574 time discounting, 574 time inconsistency:, 575 tit for tat, 530, 531 tragedy of the commons, 665 transformation function, 629 transformations, A1 transitive, 35, 121, 632, 634, 708 two-good assumption, 21 two-part tariff, 476 two-sided market, 686 two-sided matching, 329 two-sided matching models, 327 two-sided network effect, 692 two-tiered pricing, 429 U.S Constitution, 197 ultimatum game, 577 uncertainty, 217 choice under, 232 uniform pricing, 469 unit cost function, 369 unit elastic demand, 281, 286 upstream monopolist, 492 utility, 54 function, 55, 58, 61, 69 possibilities frontier, 637 possibilities set, 637 utility function concave, 227 value, 27 value at risk, 246 value of the marginal product, 487 value tax, 27, 298 VaR, 246 variable cost, 379 variable factor, 350, 360 variance, 237 A40 INDEX VCG mechanism, 711 Verizon Wireless, 677 vertical intercept, A5 Vickrey auction, 317, 319, 320, 323, 325, 330, 713 Vickrey-Clarke-Groves mechanism, 711 von Neumann-Morgenstern utility function, 224 voting mechanisms, 329 voting system, 708 wage labor, 732, 736 waiting in line, 312 Walras’ law, 592, 593, 606 Walrasian equilibrium, 590 warranty, 726 Weak Axiom of Cost Minimization (WACM), 368 Weak Axiom of Profit Maximization (WAPM), 357 Weak Axiom of Revealed Preference, 124 weak preference, 34, 47 weakly preferred set, 36 web page, 322 weighted-sum-of-utilities welfare function, 635 welfare function, 631, 642 Bergson-Samuelson, 639 individualistic, 639, 643 Rawlsian (minimax), 636 welfare maximization, 643 well-behaved indifference curves, 45 well-behaved preferences, 45, 47, 52, 186 windfall profits, 429 tax, 433 Winner’s Curse, 327 winner’s curse, 327 Yahoo, 322 zero profits, 615 zero-sum games, 546 ... between private-value auctions and common-value auctions In a private-value auction, each participant has a potentially different value for the good in question A particular piece of art may be worth... TECHNOLOGICAL CONSTRAINTS 333 and raw materials It is pretty apparent what labor, land, and raw materials mean, but capital may be a new concept Capital goods are those inputs to production that are... If you are an expert on rare stamps, with a well-known eBay member name, you may want to hold back placing your bid so as not to reveal that you are interested in a particular stamp 322 AUCTIONS